The manager of an injection moulding shop is interested in using aggregate planning to determine the shop's production levels during each of the next four quarters. The shop uses eight moulding machines to produce approximately 150 different products, employing 18 permanent workers. Because of the variety of products, standard (production) hours are used to measure demand and production. The demand forecasts (in hundred standard hours) for the next four quarters are 84, 90, 58, and 69, respectively. Each worker provides 126 standard hours per month. Up to seven temp workers can be hired. Hiring cost is $870 per worker. Labour cost (permanent or temp) is $13.50 per standard hour and overtime labour cost (by permanent workers) is $23.50 per standard hour.

Maximum overtime production is 20 percent of regular time production by permanent workers. The current inventory level is 0. Inventory carrying cost is $2.40 per standard hour per quarter, and shortage cost is $10.80 per standard hour per quarter. Assume all shortages are back ordered.

a. Show that total production standard hours by 18 permanent workers is 6,804 per quarter.

b. Show that maximum total temp standard hours is 2,646 per quarter.

c. Show that maximum total overtime standard hours is 1,361 per quarter.

d. Show that hire cost per standard hour during the first quarter of work is $2.30.

e. Calculate the beginning and ending inventories and back orders for each quarter for the plan that only uses regular permanent standard hours.

f. Using trade-off analysis, show that hiring temp workers will be cheaper than using permanent workers during overtime.

g. Consider the following two temp options (in addition to permanent worker production): Plan A: 16 hundred standard hours in Q 1 and 22 hundred standard hours in Q2; Plan B: 16 hundred standard hours in Q 1 and 21 hundred standard hours in Q2. Using trade-off analysis, show why plan B is cheaper.